
where \(\vert \Omega \vert \)  is the number of sampled entries, and \(\dim \left({\cal M}_{\mathbf {r}}\right)= \sum _{k= 1}^d r_{k-1}n_kr_k-\sum _{k = 1}^{d-1}r_k^2\)  is the degrees of freedom of an \(n_1\times \cdots \times n_d\)  tensor with TT rank \((1,r_1,\cdots ,r_{d-1},1)\) . The condition number for a tensor \({\cal X}\)  is a natural generalization of the condition number of a matrix which is defined as [1]}
\(\kappa \left({\cal X}\right)= \frac{\sigma _{\max }\left({\cal X}\right)}{\sigma _{\min }\left({\cal X}\right)},\) 
